Antisymmetrization of Geminal Wave Functions. III. Calculations of the Density Matrix and Energy of a Three-Electron Atom

The conditions, which have been discussed in two previous papers, for the antisymmetrization of a geminal-sum wave function have been applied, in a numerical example, to the calculation of the density matrix and energy of the three-electron ion ${\mathrm{Be}}^{+}$. The consequences of imposing spin symmetry upon the wave function and the effects of relaxing the antisymmetrization procedure are both discussed. A ground-state energy of -14.3024 a.u., some 0.2% above the "experimental energy," is obtained, and the corresponding density matrix given.